I think adding the ability to upgrade your Warp Core would go a long way in upgrading lower tier ships to perform better at higher levels. I could see this being the solution to the "I want to play my T2 ship as a VA" problem. Upgrading the Warp Core could provide your ship with power level increases across the board making your ship perform above its tier. Warp Cores should be expensive as well so that a player would need to work hard to upgrade their ship up a tier.

Just off the top of my head :

You could have 5 Warp Cores available, and by default each ship comes with the Warp Core that matches their tier. (Ships with their default cores would function exactly as they do now.) Once you reach a rank where a higher ship tier is made available to you, you have the ability to upgrade the Warp Core of your old ship. You can only purchase the core from a Requisitions Officer, and the core would bind on equip. (Like Starships, Warp Cores wouldn't be able to be sold because they're tied to your rank.)

For example - you fly around in your Miranda with it's Tier 1 Warp Core until you hit Lt Commander. At that point, you can get a Tier 2 ship, and you have the ability (if you have enough EC) to acquire a T2 warp core for installation into your Miranda. Installing the T2 Warp Core in your Miranda gives it the power characteristics of a T2 ship of the same class. (It has no effect on Hull points, or other ship specs.)

Each time you're promoted, you "unlock" the ability to acquire a Warp Core that corresponds to the highest tier ship available to you. So, for example, at the rank of RA, you'd be able to purchase a T5 warp core, and install it on any ship you want. While the lower tier ships won't perform as good as actual T5 ships, they will perform much better than they did with their default cores.